Study guide
6.1 Potentiometry, Ion-Selective Electrodes, and Voltammetric Techniques
PRC Chemist Licensure Examination Exam
Track your progress as you read
Finished sections get a check mark.
1 Chapter 1: Exam Overview, Chemistry Law (RA 10657), and Laboratory Safety
1.1 PRC Chemist Licensure Examination: Format, Schedule, Grading, and Passing Standards 1.2 Republic Act 10657 (Chemistry Profession Act) and Professional Ethics 1.3 Chemical Laboratory Safety, GHS Classification, Hazardous Waste Management, and Quality Assurance
2 Chapter 2: Inorganic Chemistry: Atomic Structure, Periodicity, and Chemical Bonding
2.1 Atoms, Ions, Compounds, Inorganic Nomenclature, and Stoichiometry 2.2 Quantum Numbers, Electronic Configurations, and Periodic Trends 2.3 Chemical Bonding Models: Lewis Structures, VSEPR Theory, and Molecular Polarity 2.4 Molecular Orbital Theory and Magnetochemistry of Diatomic Molecules
3 Chapter 3: Inorganic Chemistry: Coordination Compounds and Transition Metals
3.1 Coordination Chemistry: Nomenclature, Formulas, and Isomerism 3.2 Crystal Field Theory, Ligand Field Theory, d-Orbital Splitting, and Reaction Mechanisms 3.3 Electronic Absorption Spectra, Tanabe-Sugano Diagrams, and Magnetic Properties
4 Chapter 4: Inorganic Chemistry: Main Group, Reactivity, Solid State, Nuclear, and Applied Topics
4.1 Systematic Descriptive Chemistry of Main Group Elements (s- and p-Blocks) 4.2 Reactivity of Inorganic Compounds: Acid-Base Concepts, HSAB, and Redox Diagrams 4.3 Solid-State Chemistry: Crystal Systems, Unit Cells, and Band Theory 4.4 Bioinorganic Chemistry: Metalloproteins, Oxygen Carriers, and Metal Ion Toxicity 4.5 Organometallic Chemistry: 18-Electron Rule, Carbonyl Complexes, and Catalysis 4.6 Nuclear Chemistry: Stability, Decay, Transmutation, and Radioanalytical Methods 4.7 Industrial, Environmental, and Atmospheric Inorganic Chemistry and Advanced Materials
5 Chapter 5: Analytical Chemistry: Measurements, Statistics, Classical Wet Analysis, and Chemical Equilibria
5.1 Analytical Measurements: Apparatus, Units, Concentration, Sampling, and Sample Preparation 5.2 Analytical Data Evaluation: Errors, Uncertainty, Statistics, and Calibration 5.3 Gravimetric Analysis and Precipitation Equilibria ($K_{sp}$) 5.4 Neutralization Titrimetry, Polyprotic Systems, Buffers, and Alpha Fractions 5.5 Complexometric (EDTA), Redox, and Precipitation (Argentometric) Titrimetry
6 Chapter 6: Analytical Chemistry: Electroanalytical Methods and Separations
6.1 Potentiometry, Ion-Selective Electrodes, and Voltammetric Techniques 6.2 Analytical Separations: Solvent Extraction, SPE, Ion Exchange, Precipitation, Masking, and Electrodeposition 6.3 Fundamentals of Chromatography: Theoretical Plates, Resolution, and van Deemter Equation 6.4 Gas Chromatography (GC): Columns, Stationary Phases, Detectors, and Applications 6.5 High-Performance Liquid Chromatography (HPLC): Normal vs. Reversed Phase and Method Development
7 Chapter 7: Analytical Chemistry: Spectroscopic, Mass Spectrometric, and Other Instrumental Methods
7.1 Molecular UV-Vis Spectroscopy and Quantitative Beer-Lambert Law 7.2 Infrared (FTIR) and Raman Spectroscopy: Vibrational Modes and Instrumentation 7.3 Atomic Spectroscopy: Atomic Absorption (AAS) and Inductively Coupled Plasma (ICP-OES/MS) 7.4 Mass Spectrometry: Ionization Sources, Mass Analyzers, and Fragmentation Analysis 7.5 Other Instrumental Methods (XRF, Flame Emission, CE, SFC, Thermal Analysis, Electronics) and Method Selection
8 Chapter 8: Physical Chemistry: Gases, Thermodynamics, and Thermochemistry
8.1 Ideal and Real Gases and the Kinetic Molecular Theory 8.2 First Law of Thermodynamics: Heat, Work, Internal Energy, and Enthalpy 8.3 Second and Third Laws of Thermodynamics: Entropy, Carnot Engine, and Absolute Entropies 8.4 Gibbs and Helmholtz Free Energy, Spontaneity, and Fundamental Equations 8.5 Chemical Potential, Partial Molar Quantities, Fugacity, and Activity
9 Chapter 9: Physical Chemistry: Equilibrium, Phase Equilibria, Solutions, and Electrochemistry
9.1 Chemical Equilibrium: Equilibrium Constants, Le Chatelier's Principle, and the van 't Hoff Equation 9.2 Phase Rule, Phase Diagrams of One- and Two-Component Systems, and Clausius-Clapeyron Equation 9.3 Solutions: Raoult's and Henry's Laws, Colligative Properties, and Electrolytes 9.4 Electrochemistry: Galvanic Cells, Standard Potentials, and the Nernst Equation 9.5 Electrolyte Conductance, Ionic Mobility, Transport Numbers, and Concentration Cells
10 Chapter 10: Physical Chemistry: Kinetics, Surface Chemistry, and Quantum Mechanics
10.1 Reaction Rates, Rate Laws, and Integrated Rate Equations 10.2 Temperature Dependence of Rates: Arrhenius Equation, Collision Theory, and Transition State Theory 10.3 Reaction Mechanisms: Steady-State Approximation, Chain Reactions, and Catalysis 10.4 Surface Chemistry, Adsorption Isotherms, Colloids, and Macromolecular Solutions 10.5 Postulates of Quantum Mechanics, Operators, Particle in a Box, and Harmonic Oscillator 10.6 Atomic Spectra, the Hydrogen Atom, Many-Electron Atoms, and Term Symbols
11 Chapter 11: Organic Chemistry: Structure, Stereochemistry, and Hydrocarbons
11.1 Systematic IUPAC Nomenclature and Conformational Analysis of Alkanes and Cycloalkanes 11.2 Stereochemistry: Chirality, Enantiomers, Diastereomers, (R)/(S) Configuration, and Optical Activity 11.3 Alkenes and Alkynes: Addition Reactions, Markovnikov Rule, and Stereospecificity 11.4 Aromaticity: Hückel's Rule, Electrophilic Aromatic Substitution, and Directing Effects
12 Chapter 12: Organic Chemistry: Functional Groups, Mechanisms, Synthesis, and Structure Elucidation
12.1 Nucleophilic Aliphatic Substitution ($S_N1$, $S_N2$) and Elimination ($E_1$, $E_2$) Mechanisms 12.2 Alcohols, Phenols, Ethers, and Epoxides: Structure, Synthesis, and Reactivity 12.3 Carbonyl Compounds I: Aldehydes and Ketones, Nucleophilic Addition, and Oxidation/Reduction 12.4 Carbonyl Compounds II: Carboxylic Acids and Derivatives, Enolate Chemistry, and Condensations 12.5 Amines: Basicity, Synthesis, Reactions, and Arenediazonium Chemistry 12.6 Structure Elucidation: NMR Spectroscopy, Combined Spectral Problems, and Qualitative Organic Tests 12.7 Organic Synthesis Strategy, Protecting Groups, Rearrangements, and Pericyclic Reactions
13 Chapter 13: Biochemistry: Cells, Biomolecules, Enzymes, and Membranes
13.1 Cells, Organelles, Water, and Biological Acid-Base Buffers 13.2 Amino Acids, Peptides, and Hierarchical Protein Structure 13.3 Protein Purification and Biochemical Analysis of Proteins, Carbohydrates, and Lipids 13.4 Enzyme Nomenclature and Classification, Cofactors, Coenzymes, and Vitamin Precursors 13.5 Enzyme Kinetics: Michaelis-Menten Model, Lineweaver-Burk Analysis, and Enzyme Inhibition 13.6 Carbohydrates, Lipids, Biological Membranes, and Membrane Transport
14 Chapter 14: Biochemistry: Metabolism, Bioenergetics, Photosynthesis, and Molecular Genetics
14.1 Carbohydrate Catabolism and Anabolism: Glycolysis, Gluconeogenesis, Glycogen, and Pentose Phosphate Pathway 14.2 Citric Acid Cycle, Mitochondrial Electron Transport, Oxidative Phosphorylation, and $\beta$-Oxidation 14.3 Photosynthesis: Light Reactions, Photophosphorylation, and the Calvin Cycle 14.4 Lipolysis and Lipid Biosynthesis: Fatty Acids, Triacylglycerols, and Cholesterol 14.5 Nitrogen Metabolism: Nitrogen Fixation, Amino Acid Metabolism, and the Urea Cycle 14.6 Nucleic Acids, DNA Replication, Transcription, Translation, and Recombinant DNA Techniques 14.7 Regulation of Gene Expression, Mutation and Mutagens, DNA Repair, Carcinogenesis, and cDNA Cloning
6.1 Potentiometry, Ion-Selective Electrodes, and Voltammetric Techniques
Key Takeaways Explain This Topic AI
Potentiometry measures equilibrium galvanic cell potential under zero-current flow ( i = 0 i = 0 i = 0 ), relating indicator potential to analyte activity via the Nernst and Nikolsky-Eisenman equations.
Standard reference electrodes provide known, invariant half-cell potentials: the Standard Hydrogen Electrode (SHE, defined as 0.000 V 0.000\text{ V} 0.000 V ), Saturated Calomel Electrode (SCE, E = + 0.244 V E = +0.244\text{ V} E = + 0.244 V vs. SHE at 25 ∘ C 25^\circ\text{C} 2 5 ∘ C ), and Silver/Silver Chloride electrode ( A g / A g C l Ag/AgCl A g / A g Cl in sat. K C l KCl K Cl , E = + 0.197 V E = +0.197\text{ V} E = + 0.197 V vs. SHE).
The glass membrane p H pH p H electrode exhibits boundary potentials across inner and outer hydrated silica gel layers; it suffers from alkaline error (sodium error, falsely low p H pH p H ) at p H > 10 pH > 10 p H > 10 and acid error (falsely high p H pH p H ) at p H < 1 pH < 1 p H < 1 .
The fluoride crystal membrane electrode ( L a F 3 LaF_3 L a F 3 doped with E u 2 + Eu^{2+} E u 2 + ) operates optimally between p H 5 and 7 pH\ 5\text{ and }7 p H 5 and 7 in Total Ionic Strength Adjustment Buffer (TISAB), which buffers p H pH p H , fixes ionic strength, and uses CDTA to release fluoride from F e 3 + Fe^{3+} F e 3 + and A l 3 + Al^{3+} A l 3 + complexes.
Cyclic voltammetry uses a three-electrode cell (working, reference, counter) with a supporting electrolyte to suppress migration; a reversible redox couple at 25 ∘ C 25^\circ\text{C} 2 5 ∘ C displays peak separation Δ E p = 59.2 / n mV \Delta E_p = 59.2/n\text{ mV} Δ E p = 59.2/ n mV , current ratio i p a / i p c = 1.0 i_{pa}/i_{pc} = 1.0 i p a / i p c = 1.0 , and peak current governed by the Randles-Ševčík equation.
Last updated: October 2026
6.1 Potentiometry, Ion-Selective Electrodes, and Voltammetric Techniques
Quick Answer: Electroanalytical methods measure electrical signals (potential, current, charge, or conductance) to determine analyte concentration and chemical speciation. Potentiometry measures cell potential at zero net current ( i = 0 i = 0 i = 0 ) using indicator electrodes (such as glass p H pH p H and L a F 3 LaF_3 L a F 3 fluoride electrodes) referenced against standard half-cells (SCE, A g / A g C l Ag/AgCl A g / A g Cl ). Dynamic techniques apply controlled potentials: Cyclic Voltammetry (CV) diagnoses redox reversibility ( Δ E p = 59.2 / n mV \Delta E_p = 59.2/n\text{ mV} Δ E p = 59.2/ n mV at 25 ∘ C 25^\circ\text{C} 2 5 ∘ C ), while Anodic Stripping Voltammetry (ASV) preconcentrates trace heavy metals for sub-ppb quantitation. Coulometry applies Faraday's laws ( Q = n F N Q = nFN Q = n FN ) for absolute standardless quantification.
Taxonomy of Electroanalytical Methods
Electroanalytical techniques are categorized based on whether an external current flows through the electrochemical cell and whether electrical control is maintained over potential or current:
Technique Current Regime Excitation Signal Measured Variable Governing Equation / Basis
Potentiometry Zero current ( i = 0 i = 0 i = 0 ) Spontaneous equilibrium potential Cell potential ( E cell E_{\text{cell}} E cell ) Nernst equation: E = E ∘ − 0.0592 n log Q E = E^\circ - \frac{0.0592}{n}\log Q E = E ∘ − n 0.0592 lo g Q
Voltammetry Controlled dynamic current ( i > 0 i > 0 i > 0 ) Controlled potential sweep ( E E E vs. t t t ) Current ( i i i ) as a function of E E E Randles-Ševčík, Ilkovič, Cottrell equations
Amperometry Controlled dynamic current ( i > 0 i > 0 i > 0 ) Constant applied potential ( E applied E_{\text{applied}} E applied ) Current ( i i i ) over time ( t t t ) Limiting diffusion current ( i d ∝ C analyte i_d \propto C_{\text{analyte}} i d ∝ C analyte )
Coulometry Dynamic current ( i > 0 i > 0 i > 0 ) Constant potential or constant current Total charge ( Q Q Q in coulombs) Faraday's law: Q = ∫ i d t = n F N Q = \int i dt = nFN Q = ∫ i d t = n FN
Conductometry High-frequency AC ( i > 0 i > 0 i > 0 ) Alternating potential ( ∼ 1 kHz \sim 1\text{ kHz} ∼ 1 kHz ) Electrolytic conductance ( G = 1 / R G = 1/R G = 1/ R ) Ohm's law & Kohlrausch's law of ionic mobility
Potentiometric Cell Architecture and Reference Electrodes
A potentiometric cell comprises an indicator electrode (whose half-cell potential responds directly to analyte activity a A a_A a A ), a reference electrode (with a known, invariant potential independent of solution composition), and a salt bridge that establishes electrolytic contact while minimizing the liquid junction potential ( E j E_j E j ):
E cell = E indicator − E reference + E j E_{\text{cell}} = E_{\text{indicator}} - E_{\text{reference}} + E_j E cell = E indicator − E reference + E j
Because the junction potential across typical saturated K C l KCl K Cl bridges is small and reproducible (typically 1 − 3 mV 1-3\text{ mV} 1 − 3 mV ), calibration against primary chemical standards absorbs E j E_j E j and E reference E_{\text{reference}} E reference into a constant cell parameter. High-Impedance Voltmeter (Input Impedance > 10^12 Ohms)
- [ E_cell = E_ind - E_ref + E_j ]
- / \
- / \
- [Reference Electrode] [Indicator Electrode]
- (SCE or Ag/AgCl) (Glass, Metal, or ISE)
- | |
- [Sat. KCl Salt Bridge] |
- \ /
- [ Analyte Solution Containing Target Ion A ]
- Standard Reference Electrodes
Standard Hydrogen Electrode (SHE):
Architecture: Platinized platinum foil immersed in an aqueous solution of unit hydrogen ion activity ( a H + = 1.00 M a_{H^+} = 1.00\text{ M} a H + = 1.00 M ) bubbling with pure hydrogen gas at standard state ( P H 2 = 1.00 bar = 100 kPa P_{H_2} = 1.00\text{ bar} = 100\text{ kPa} P H 2 = 1.00 bar = 100 kPa ).
Cell notation: P t ( s ) ∣ H 2 ( g , 1 bar ) ∣ H + ( a q , a = 1.00 M ) ∥ Pt(s) \mid H_2(g, 1\text{ bar}) \mid H^+(aq, a=1.00\text{ M}) \parallel Pt ( s ) ∣ H 2 ( g , 1 bar ) ∣ H + ( a q , a = 1.00 M ) ∥
Absolute assignment: E ∘ = 0.000 V E^\circ = 0.000\text{ V} E ∘ = 0.000 V at all temperatures. Serving as the thermodynamic benchmark, it is rarely used in routine industrial or regulatory testing due to H 2 H_2 H 2 explosion hazards, difficulty maintaining unit activity, and platinum catalyst poisoning by trace sulfides, arsenic, or organic vapors.
Saturated Calomel Electrode (SCE):
Architecture: Liquid mercury in contact with a paste of mercury(I) chloride (calomel, H g 2 C l 2 Hg_2Cl_2 H g 2 C l 2 ) and a saturated solution of potassium chloride ( K C l , ∼ 4.6 M KCl, \sim 4.6\text{ M} K Cl , ∼ 4.6 M at 25 ∘ C 25^\circ\text{C} 2 5 ∘ C ).
Cell notation: H g ( l ) ∣ H g 2 C l 2 ( s ) ∣ K C l ( a q , sat. ) ∥ Hg(l) \mid Hg_2Cl_2(s) \mid KCl(aq, \text{sat.}) \parallel H g ( l ) ∣ H g 2 C l 2 ( s ) ∣ K Cl ( a q , sat. ) ∥
Half-cell reduction: H g 2 C l 2 ( s ) + 2 e − ⇌ 2 H g ( l ) + 2 C l − ( a q ) Hg_2Cl_2(s) + 2e^- \rightleftharpoons 2Hg(l) + 2Cl^-(aq) H g 2 C l 2 ( s ) + 2 e − ⇌ 2 H g ( l ) + 2 C l − ( a q )
Standard reduction potential: E = + 0.2444 V E = +0.2444\text{ V} E = + 0.2444 V vs. SHE at 25 ∘ C 25^\circ\text{C} 2 5 ∘ C .
Temperature coefficient: E t = 0.2444 − 6.6 × 10 − 4 ( T − 25 ) E_t = 0.2444 - 6.6 \times 10^{-4}(T - 25) E t = 0.2444 − 6.6 × 1 0 − 4 ( T − 25 ) . Note that calomel undergoes irreversible disproportionation at temperatures exceeding 65 ∘ C 65^\circ\text{C} 6 5 ∘ C .
Silver/Silver Chloride Electrode ( A g / A g C l Ag/AgCl A g / A g Cl ):
Architecture: A silver wire coated with a porous layer of silver chloride ( A g C l AgCl A g Cl ) immersed in a K C l KCl K Cl electrolyte solution.
Cell notation: A g ( s ) ∣ A g C l ( s ) ∣ K C l ( a q , sat. or 3.5 M ) ∥ Ag(s) \mid AgCl(s) \mid KCl(aq, \text{sat. or } 3.5\text{ M}) \parallel A g ( s ) ∣ A g Cl ( s ) ∣ K Cl ( a q , sat. or 3.5 M ) ∥
Half-cell reduction: A g C l ( s ) + e − ⇌ A g ( s ) + C l − ( a q ) AgCl(s) + e^- \rightleftharpoons Ag(s) + Cl^-(aq) A g Cl ( s ) + e − ⇌ A g ( s ) + C l − ( a q )
Potential values vs. SHE at 25 ∘ C 25^\circ\text{C} 2 5 ∘ C :
- Saturated K C l KCl K Cl : E = + 0.197 V E = +0.197\text{ V} E = + 0.197 V
- 3.5 M K C l 3.5\text{ M } KCl 3.5 M K Cl : E = + 0.205 V E = +0.205\text{ V} E = + 0.205 V
1.0 M K C l 1.0\text{ M } KCl 1.0 M K Cl : E ≈ + 0.235 V E \approx +0.235\text{ V} E ≈ + 0.235 V (the standard potential at unit chloride activity is + 0.222 V +0.222\text{ V} + 0.222 V )
Practical advantages: Usable above 60 ∘ C 60^\circ\text{C} 6 0 ∘ C , where calomel electrodes become unreliable; non-toxic compared to mercury calomel electrodes, and easily miniaturized into combination p H pH p H probes.
Converting Between Reference Scales
Reduction potentials are often reported relative to an SCE or A g / A g C l Ag/AgCl A g / A g Cl reference rather than SHE. The conversion requires adding the reference potential:
E vs. SHE = E vs. SCE + 0.244 V E_{\text{vs. SHE}} = E_{\text{vs. SCE}} + 0.244\text{ V} E vs. SHE = E vs. SCE + 0.244 V E vs. SHE = E vs. Ag/AgCl (sat.) + 0.197 V E_{\text{vs. SHE}} = E_{\text{vs. Ag/AgCl (sat.)}} + 0.197\text{ V} E vs. SHE = E vs. Ag/AgCl (sat.) + 0.197 V
Worked Example: A cyclic voltammetric reduction peak is recorded at − 0.452 V -0.452\text{ V} − 0.452 V vs. SCE at 25 ∘ C 25^\circ\text{C} 2 5 ∘ C . Calculate this peak potential relative to (a) the Standard Hydrogen Electrode (SHE), and (b) a saturated A g / A g C l Ag/AgCl A g / A g Cl reference electrode.
Part (a): Potential vs. SHE E vs. SHE = − 0.452 V + 0.244 V = − 0.208 V E_{\text{vs. SHE}} = -0.452\text{ V} + 0.244\text{ V} = -0.208\text{ V} E vs. SHE = − 0.452 V + 0.244 V = − 0.208 V
Part (b): Potential vs. Saturated A g / A g C l Ag/AgCl A g / A g Cl E vs. Ag/AgCl = E vs. SHE − 0.197 V = − 0.208 V − 0.197 V = − 0.405 V E_{\text{vs. Ag/AgCl}} = E_{\text{vs. SHE}} - 0.197\text{ V} = -0.208\text{ V} - 0.197\text{ V} = -0.405\text{ V} E vs. Ag/AgCl = E vs. SHE − 0.197 V = − 0.208 V − 0.197 V = − 0.405 V
Indicator Electrodes: Metallic and Redox Types
Indicator electrodes respond dynamically to the activity of an electroactive species in solution:
Electrodes of the First Kind: A pure metal in equilibrium with its own cation (e.g., A g / A g + Ag/Ag^+ A g / A g + , C u / C u 2 + Cu/Cu^{2+} C u / C u 2 + , P b / P b 2 + Pb/Pb^{2+} P b / P b 2 + ): M n + + n e − ⇌ M ( s ) ⟹ E = E M n + / M ∘ − 0.0592 n log 1 a M n + = E ∘ + 0.0592 n log a M n + M^{n+} + ne^- \rightleftharpoons M(s) \implies E = E^\circ_{M^{n+}/M} - \frac{0.0592}{n}\log \frac{1}{a_{M^{n+}}} = E^\circ + \frac{0.0592}{n}\log a_{M^{n+}} M n + + n e − ⇌ M ( s ) ⟹ E = E M n + / M ∘ − n 0.0592 lo g a M n + 1 = E ∘ + n 0.0592 lo g a M n + Limitations: Poor selectivity (easily oxidized by dissolved O 2 O_2 O 2 ), slow electron transfer kinetics, and restricted to soft metals ( A g , C u , P b , C d , Z n , B i , T l Ag, Cu, Pb, Cd, Zn, Bi, Tl A g , C u , P b , C d , Z n , B i , Tl ). Hard metals ( F e , C o , N i , C r Fe, Co, Ni, Cr F e , C o , N i , C r ) exhibit irreversible, non-reproducible potentials.
Electrodes of the Second Kind: A metal in contact with an insoluble salt of its cation and excess anion, responding to anion activity (e.g., A g / A g C l / C l − Ag/AgCl/Cl^- A g / A g Cl / C l − , H g / H g 2 C l 2 / C l − Hg/Hg_2Cl_2/Cl^- H g / H g 2 C l 2 / C l − , A g / A g 2 S / S 2 − Ag/Ag_2S/S^{2-} A g / A g 2 S / S 2 − ): A g C l ( s ) + e − ⇌ A g ( s ) + C l − ( a q ) ⟹ E = E A g C l / A g ∘ − 0.0592 log a C l − AgCl(s) + e^- \rightleftharpoons Ag(s) + Cl^-(aq) \implies E = E^\circ_{AgCl/Ag} - 0.0592\log a_{Cl^-} A g Cl ( s ) + e − ⇌ A g ( s ) + C l − ( a q ) ⟹ E = E A g Cl / A g ∘ − 0.0592 lo g a C l −
Electrodes of the Third Kind: A metal electrode whose potential responds to a different cation via two coupled homogeneous equilibria (e.g., a mercury electrode in a solution containing H g − E D T A 2 − Hg-EDTA^{2-} H g − E D T A 2 − , C a − E D T A 2 − Ca-EDTA^{2-} C a − E D T A 2 − , and free C a 2 + Ca^{2+} C a 2 + ions responds to a C a 2 + a_{Ca^{2+}} a C a 2 + ).
Inert Redox Electrodes: Chemically inert conductors ( P t , A u Pt, Au Pt , A u , glassy carbon, graphite) that do not participate in the redox reaction but act as an electron source or sink for redox couples in solution (e.g., F e 3 + / F e 2 + Fe^{3+} / Fe^{2+} F e 3 + / F e 2 + or C e 4 + / C e 3 + Ce^{4+} / Ce^{3+} C e 4 + / C e 3 + ): E = E F e 3 + / F e 2 + ∘ − 0.0592 log a F e 2 + a F e 3 + E = E^\circ_{Fe^{3+}/Fe^{2+}} - 0.0592 \log \frac{a_{Fe^{2+}}}{a_{Fe^{3+}}} E = E F e 3 + / F e 2 + ∘ − 0.0592 lo g a F e 3 + a F e 2 +
Ion-Selective Electrodes (ISE) and Membrane Potentials
Ion-Selective Electrodes respond selectively to specific ionic activities across a semipermeable, ion-conducting membrane without involving redox transformations. The potential developed across the membrane is a phase-boundary potential generated by ion-exchange equilibrium at the two membrane interfaces.
The Glass Membrane pH Electrode
The standard glass electrode employs a thin bulb ( 0.03 − 0.1 mm 0.03-0.1\text{ mm} 0.03 − 0.1 mm ) of lithium silicate or Corning 015 glass ( 72 % S i O 2 , 22 % N a 2 O , 6 % C a O 72\%\text{ } SiO_2, 22\%\text{ } Na_2O, 6\%\text{ } CaO 72% S i O 2 , 22% N a 2 O , 6% C a O ).
Hydrated Gel Layers: When soaked in water, alkali ions ( N a + Na^+ N a + or L i + Li^+ L i + ) in the outer 10 − 100 nm 10-100\text{ nm} 10 − 100 nm layer of the three-dimensional silicate lattice exchange with H + H^+ H + from the solution: Glass − − N a + ( s ) + H + ( a q ) ⇌ Glass − − H + ( s ) + N a + ( a q ) \text{Glass}^- - Na^+(s) + H^+(aq) \rightleftharpoons \text{Glass}^- - H^+(s) + Na^+(aq) Glass − − N a + ( s ) + H + ( a q ) ⇌ Glass − − H + ( s ) + N a + ( a q )
Both the outer and inner glass surfaces form hydrated silicic acid gel layers separated by an anhydrous central glass core ( 0.05 mm ~0.05\text{ mm} 0.05 mm ) that conducts current solely by interstitial hopping of N a + Na^+ N a + or L i + Li^+ L i + ions under high electrical resistance ( 10 7 − 10 9 Ω 10^7-10^9\text{ }\Omega 1 0 7 − 1 0 9 Ω ).
The total membrane boundary potential ( E b E_b E b ) depends on the ratio of hydrogen ion activities in the external test solution ( a 1 a_1 a 1 ) and the internal reference solution ( a 2 a_2 a 2 , typically 0.1 M H C l 0.1\text{ M } HCl 0.1 M H Cl ): E b = E 1 − E 2 = 0.0592 log a 1 a 2 = 0.0592 log a 1 − 0.0592 log a 2 E_b = E_1 - E_2 = 0.0592\log \frac{a_1}{a_2} = 0.0592\log a_1 - 0.0592\log a_2 E b = E 1 − E 2 = 0.0592 lo g a 2 a 1 = 0.0592 lo g a 1 − 0.0592 lo g a 2 Internal Buffer/Cl- | Glass Gel (Inner) | Anhydrous Glass Core | Glass Gel (Outer) | External Analyte
- (a2 = constant) | (H+ Exchange) | (Na+ Hop) | (H+ Exchange) | (a1 = variable)
- Systematic Operational Errors of the Glass Electrode
Alkaline Error (Sodium Error): At high p H pH p H ( p H > 10 − 12 pH > 10-12 p H > 10 − 12 ) in solutions with low [ H + ] [H^+] [ H + ] and elevated [ N a + ] [Na^+] [ N a + ] or [ K + ] [K^+] [ K + ] , the glass membrane loses exclusivity for H + H^+ H + and exchanges competitively with N a + Na^+ N a + . Because the electrode responds as if extra H + H^+ H + were present, the instrument registers a falsely low p H pH p H (e.g., true p H = 12.00 pH = 12.00 p H = 12.00 , measured p H = 11.65 pH = 11.65 p H = 11.65 ). Lithia glasses ( L i 2 O Li_2O L i 2 O replacing N a 2 O Na_2O N a 2 O ) significantly reduce alkaline error up to p H 13.5 pH\ 13.5 p H 13.5 .
Acid Error: In concentrated acidic media ( p H < 0.5 − 1.0 pH < 0.5-1.0 p H < 0.5 − 1.0 ), water activity ( a H 2 O a_{H_2O} a H 2 O ) drops below unity, altering the structure of the outer hydrated gel layer and causing the electrode to register a falsely high p H pH p H .
Asymmetry Potential: A residual potential ( 1 − 5 mV 1-5\text{ mV} 1 − 5 mV ) observed across the membrane when identical solutions are placed on both sides of the glass bulb. It arises from unequal mechanical strain during blowing, structural defects, inner vs. outer surface etching, and contamination. Asymmetry potential is completely eliminated by routine two-point calibration (bracketing) using standard buffer solutions (e.g., p H 4.01 , 7.00 pH\ 4.01, 7.00 p H 4.01 , 7.00 , or 10.01 10.01 10.01 ).
Dehydration: Storing a glass electrode dry dehydrates the outer silicate gel, leading to erratic, drift-prone potentials and sluggish response times. Electrodes must be stored in saturated K C l KCl K Cl or commercial storage solution.
The Nikolsky-Eisenman Equation
When an interfering ion B B B with charge z B z_B z B competes with primary analyte ion A A A with charge z A z_A z A , the membrane potential follows the Nikolsky-Eisenman equation :
E = constant + 0.05916 z A log ( a A + ∑ B K A , B pot ( a B ) z A / z B ) E = \text{constant} + \frac{0.05916}{z_A} \log \left( a_A + \sum_B K_{A,B}^{\text{pot}} (a_B)^{z_A / z_B} \right) E = constant + z A 0.05916 lo g ( a A + ∑ B K A , B pot ( a B ) z A / z B )
where K A , B pot K_{A,B}^{\text{pot}} K A , B pot is the potentiometric selectivity coefficient :
K A , B pot < 1 K_{A,B}^{\text{pot}} < 1 K A , B pot < 1 : The electrode preferentially detects target analyte A A A over interferent B B B .
K A , B pot > 1 K_{A,B}^{\text{pot}} > 1 K A , B pot > 1 : The electrode responds more strongly to interferent B B B than to target ion A A A .
For a high-performance electrode, K A , B pot K_{A,B}^{\text{pot}} K A , B pot should be as small as possible (ideally < 10 − 4 < 10^{-4} < 1 0 − 4 ).
Worked Example: A potassium ion-selective liquid membrane electrode exhibits a selectivity coefficient K K + , N a + pot = 2.5 × 10 − 4 K_{K^+, Na^+}^{\text{pot}} = 2.5 \times 10^{-4} K K + , N a + pot = 2.5 × 1 0 − 4 . Calculate the percentage relative error in determining potassium activity in a serum sample containing a K + = 4.0 × 10 − 3 M a_{K^+} = 4.0 \times 10^{-3}\text{ M} a K + = 4.0 × 1 0 − 3 M and a N a + = 0.140 M a_{Na^+} = 0.140\text{ M} a N a + = 0.140 M .
The effective apparent potassium activity is: a K + , apparent = a K + + K K + , N a + pot ⋅ a N a + = ( 4.0 × 10 − 3 ) + ( 2.5 × 10 − 4 × 0.140 ) a_{K^+, \text{apparent}} = a_{K^+} + K_{K^+, Na^+}^{\text{pot}} \cdot a_{Na^+} = (4.0 \times 10^{-3}) + (2.5 \times 10^{-4} \times 0.140) a K + , apparent = a K + + K K + , N a + pot ⋅ a N a + = ( 4.0 × 1 0 − 3 ) + ( 2.5 × 1 0 − 4 × 0.140 ) a K + , apparent = 4.0 × 10 − 3 + 3.5 × 10 − 5 = 4.035 × 10 − 3 M a_{K^+, \text{apparent}} = 4.0 \times 10^{-3} + 3.5 \times 10^{-5} = 4.035 \times 10^{-3}\text{ M} a K + , apparent = 4.0 × 1 0 − 3 + 3.5 × 1 0 − 5 = 4.035 × 1 0 − 3 M
Percentage error: % Error = 4.035 × 10 − 3 − 4.000 × 10 − 3 4.000 × 10 − 3 × 100 % = 3.5 × 10 − 5 4.0 × 10 − 3 × 100 % = + 0.875 % \%\text{ Error} = \frac{4.035 \times 10^{-3} - 4.000 \times 10^{-3}}{4.000 \times 10^{-3}} \times 100\% = \frac{3.5 \times 10^{-5}}{4.0 \times 10^{-3}} \times 100\% = +0.875\% % Error = 4.000 × 1 0 − 3 4.035 × 1 0 − 3 − 4.000 × 1 0 − 3 × 100% = 4.0 × 1 0 − 3 3.5 × 1 0 − 5 × 100% = + 0.875% Conclusion: The sodium interference causes an error of less than 1 % 1\% 1% , which is analytically acceptable for physiological serum electrolytes.
Liquid Membrane and Solid-State Crystal Membrane Electrodes
Liquid Membrane Electrodes (Polymer Matrix ISEs):
Potassium Ion-Selective Electrode: Employs the neutral macrocyclic depsipeptide valinomycin dissolved in a plasticized PVC membrane. Valinomycin features a hydrophobic exterior and a hydrophilic cavity lined with six carbonyl oxygens whose coordination dimensions match the unhydrated crystal ionic radius of K + K^+ K + ( 1.38 A ˚ 1.38\text{ }\text{\AA} 1.38 A ˚ ) with extreme precision. Its selectivity over N a + Na^+ N a + ( K K + , N a + pot ≈ 10 − 4 K_{K^+, Na^+}^{\text{pot}} \approx 10^{-4} K K + , N a + pot ≈ 1 0 − 4 ) is unmatched, permitting direct clinical assay of potassium in whole blood.
Calcium Ion-Selective Electrode: Employs an immobilized liquid ion exchanger, such as calcium bis(di-n-octylphenylphosphate), dissolved in PVC. It responds to C a 2 + Ca^{2+} C a 2 + down to 10 − 6 M 10^{-6}\text{ M} 1 0 − 6 M and discriminates against M g 2 + Mg^{2+} M g 2 + and N a + Na^+ N a + .
Solid-State Crystal Membrane Electrodes:
Fluoride Electrode ( L a F 3 LaF_3 L a F 3 Crystal): Employs a single crystal disk of lanthanum trifluoride ( L a F 3 LaF_3 L a F 3 ) doped with europium difluoride ( E u F 2 EuF_2 E u F 2 , ∼ 0.5 % \sim 0.5\% ∼ 0.5% ). Doping divalent E u 2 + Eu^{2+} E u 2 + for trivalent L a 3 + La^{3+} L a 3 + introduces structural anion lattice vacancies through which F − F^- F − ions migrate across the crystal lattice by vacancy hopping.
Chemical Interferences: Hydroxide ion ( O H − OH^- O H − ) is the sole significant chemical interferent because its ionic radius ( 1.33 A ˚ 1.33\text{ }\text{\AA} 1.33 A ˚ ) and single negative charge nearly mirror fluoride ( 1.36 A ˚ 1.36\text{ }\text{\AA} 1.36 A ˚ ). At p H > 8 pH > 8 p H > 8 , O H − OH^- O H − precipitates L a ( O H ) 3 La(OH)_3 L a ( O H ) 3 at the crystal face, releasing excess F − F^- F − and causing a massive positive error. Conversely, at p H < 5 pH < 5 p H < 5 , F − F^- F − protonates to form weak acids ( H F HF H F , p K a = 3.17 pK_a = 3.17 p K a = 3.17 , and H F 2 − HF_2^- H F 2 − ), which do not register on the crystal membrane, yielding a falsely low fluoride readout.
Total Ionic Strength Adjustment Buffer (TISAB): Routine determination of fluoride in fluoridated municipal water and dental formulations requires a 1 : 1 1:1 1 : 1 volume dilution with TISAB. TISAB contains:
Acetate Buffer ( p H 5.0 − 5.5 pH\ 5.0-5.5 p H 5.0 − 5.5 ): Maintains solution p H pH p H strictly between 5 5 5 and 7 7 7 to avoid both O H − OH^- O H − interference and H F HF H F formation.
High Concentration N a C l NaCl N a Cl ( 1.0 M 1.0\text{ M} 1.0 M ): Fixes the total ionic strength ( μ \mu μ ) so that the activity coefficient γ F − \gamma_{F^-} γ F − remains constant across all calibration standards and unknown samples, equating activity to molar concentration ( a F − = γ F − [ F − ] a_{F^-} = \gamma_{F^-} [F^-] a F − = γ F − [ F − ] ).
Chelating Agent (CDTA or EDTA): Preferentially complexes polyvalent cations ( F e 3 + , A l 3 + , S i 4 + Fe^{3+}, Al^{3+}, Si^{4+} F e 3 + , A l 3 + , S i 4 + ) that strongly bind fluoride ( [ F e F ] 2 + , [ A l F 6 ] 3 − [FeF]^{2+}, [AlF_6]^{3-} [ F e F ] 2 + , [ A l F 6 ] 3 − ), releasing all bound fluoride into free, detectable F − F^- F − form.
Voltammetric Techniques and the Three-Electrode Cell
Unlike zero-current potentiometry, voltammetry is a dynamic method where a controlled potential waveform is impressed upon a micro working electrode while the resulting electrolysis current ( i i i ) is measured as a function of potential ( E E E ). Potentiostat / Galvanostat
- [ Voltage Generator / i-to-V ]
- / | \
- / | \
- [Counter/Auxiliary] [Reference] [Working Electrode]
- (Pt wire/coil) (Ag/AgCl or SCE) (Glassy C, Pt, Au, HMDE)
- | | |
- \ | /
- +-------------------+---------------------+
- | Cell: Analyte + 0.1 M Supporting Salt |
- +-----------------------------------------+
- The Three-Electrode Architecture
In early two-electrode cells, current passing through the reference electrode induced concentration polarization and caused an uncompensated ohmic drop ( i R cell iR_{\text{cell}} i R cell ), changing the reference potential. Modern voltammetry isolates the circuit using three dedicated electrodes:
Working Electrode (WE): The micro-electrode (surface area ∼ 0.01 − 0.2 cm 2 \sim 0.01-0.2\text{ cm}^2 ∼ 0.01 − 0.2 cm 2 ) where the redox reaction of the analyte occurs. Substrates include glassy carbon (broad anodic and cathodic potential window), platinum, gold, boron-doped diamond (BDD), and mercury (Hanging Mercury Drop Electrode HMDE or Thin Mercury Film Electrode TMFE; exceptional high hydrogen overpotential allowing cathodic sweeps down to − 1.8 V -1.8\text{ V} − 1.8 V ).
Reference Electrode (RE): ( A g / A g C l Ag/AgCl A g / A g Cl or SCE) Positioned with its Luggin capillary tip placed immediately adjacent to the working electrode surface to minimize solution resistance. The potentiostat's high-input-impedance operational amplifier ensures zero net current flows through the reference electrode, preserving its thermodynamic half-cell potential.
Counter / Auxiliary Electrode (CE): A high-surface-area inert conductor (platinum coil or graphite rod) that completes the current circuit with the working electrode. The current flowing through the working electrode is balanced by an equal and opposite current at the counter electrode.
Role of the Supporting Electrolyte
Voltammetric solutions require a large excess ( 0.1 − 1.0 M 0.1-1.0\text{ M} 0.1 − 1.0 M ) of an electrochemically inactive salt (e.g., K N O 3 , K C l , N a C l O 4 KNO_3, KCl, NaClO_4 K N O 3 , K Cl , N a Cl O 4 , or tetraalkylammonium salts like T B A P F 6 TBAPF_6 TB A P F 6 for non-aqueous solvents):
Suppression of Migration Current: Eliminates electrostatic attraction/repulsion between charged ions and the charged electrode surface. The supporting electrolyte ions carry > 99.9 % >99.9\% > 99.9% of electrostatic charge migration, ensuring analyte mass transport occurs solely by diffusion (governed by Fick's laws).
Elimination of Ohmic i R iR i R Drop: Decreases bulk solution electrical resistance ( R R R ).
Buffer and Ionic Strength Stabilization: Holds activity coefficients and double-layer capacitance constant.
Cyclic Voltammetry (CV): Diagnostic Criteria of Reversibility
Cyclic Voltammetry applies a triangular potential excitation waveform to the working electrode, sweeping from an initial potential E 1 E_1 E 1 to a switching potential E 2 E_2 E 2 at a linear scan rate ( ν = d E / d t \nu = dE/dt ν = d E / d t , typically 10 − 1000 mV/s 10-1000\text{ mV/s} 10 − 1000 mV/s ), then reversing the sweep back to E 1 E_1 E 1 .
Forward Sweep: O + n e − → cathodic reduction R ( producing cathodic peak current i p c at E p c ) \text{Forward Sweep: } O + ne^- \xrightarrow{\text{cathodic reduction}} R \quad (\text{producing cathodic peak current } i_{pc} \text{ at } E_{pc}) Forward Sweep: O + n e − cathodic reduction R ( producing cathodic peak current i p c at E p c ) Reverse Sweep: R → anodic oxidation O + n e − ( producing anodic peak current i p a at E p a ) \text{Reverse Sweep: } R \xrightarrow{\text{anodic oxidation}} O + ne^- \quad (\text{producing anodic peak current } i_{pa} \text{ at } E_{pa}) Reverse Sweep: R anodic oxidation O + n e − ( producing anodic peak current i p a at E p a )
Diagnostic Criteria for an Electrochemically Reversible Redox Couple at 25 ∘ C 25^\circ\text{C} 2 5 ∘ C
For a diffusion-controlled, reversible Nernstian electron transfer ( O + n e − ⇌ R O + ne^- \rightleftharpoons R O + n e − ⇌ R ):
Peak Potential Separation ( Δ E p \Delta E_p Δ E p ): Δ E p = ∣ E p a − E p c ∣ = 0.0592 V n = 59.2 mV n \Delta E_p = |E_{pa} - E_{pc}| = \frac{0.0592\text{ V}}{n} = \frac{59.2\text{ mV}}{n} Δ E p = ∣ E p a − E p c ∣ = n 0.0592 V = n 59.2 mV
For a 1 1 1 -electron transfer ( n = 1 n = 1 n = 1 ): Δ E p ≈ 59 mV \Delta E_p \approx 59\text{ mV} Δ E p ≈ 59 mV (experimentally 58 − 65 mV 58-65\text{ mV} 58 − 65 mV due to small residual uncompensated resistance).
For a 2 2 2 -electron transfer ( n = 2 n = 2 n = 2 ): Δ E p ≈ 29.6 mV ≈ 30 mV \Delta E_p \approx 29.6\text{ mV} \approx 30\text{ mV} Δ E p ≈ 29.6 mV ≈ 30 mV .
Δ E p \Delta E_p Δ E p is independent of scan rate ( ν \nu ν ) for a reversible system. If Δ E p \Delta E_p Δ E p increases markedly as scan rate increases, the electron transfer kinetics are quasi-reversible or irreversible (governed by Butler-Volmer kinetics).
Formal Reduction Potential ( E 0 ′ E^{0\prime} E 0′ ): E 0 ′ = E p a + E p c 2 E^{0\prime} = \frac{E_{pa} + E_{pc}}{2} E 0′ = 2 E p a + E p c The formal potential is located midway between the anodic and cathodic peak potentials.
Peak Current Ratio: ∣ i p a i p c ∣ = 1.0 \left| \frac{i_{pa}}{i_{pc}} \right| = 1.0 i p c i p a = 1.0 The ratio of anodic to cathodic peak heights is unity, confirming that the reduced intermediate R R R is chemically stable and does not undergo follow-up chemical decay (such as EC mechanisms).
Scan Rate Dependence (The Randles-Ševčík Equation): At 298 K 298\text{ K} 298 K ( 25 ∘ C 25^\circ\text{C} 2 5 ∘ C ), the peak current for a reversible process is governed by: i p = ( 2.69 × 10 5 ) n 3 / 2 A D 1 / 2 C ∗ ν 1 / 2 i_p = (2.69 \times 10^5) \, n^{3/2} \, A \, D^{1/2} \, C^* \, \nu^{1/2} i p = ( 2.69 × 1 0 5 ) n 3/2 A D 1/2 C ∗ ν 1/2 where i p i_p i p is peak current (Amperes), n n n is number of transferred electrons, A A A is electrode surface area ( cm 2 \text{cm}^2 cm 2 ), D D D is diffusion coefficient ( cm 2 / s \text{cm}^2/\text{s} cm 2 / s ), C ∗ C^* C ∗ is bulk analyte concentration ( mol/cm 3 \text{mol/cm}^3 mol/cm 3 ), and ν \nu ν is potential scan rate ( V/s \text{V/s} V/s ).
A linear plot of i p i_p i p versus ν 1 / 2 \nu^{1/2} ν 1/2 passing through the origin is the gold-standard proof that the electrode process is controlled purely by diffusion rather than surface adsorption or catalytic cycles.
Stripping Voltammetry and Heavy Metal Analysis
Stripping Voltammetry is the most sensitive electroanalytical technique available, routinely achieving detection limits in the sub-ppb ( 10 − 9 − 10 − 11 M 10^{-9}-10^{-11}\text{ M} 1 0 − 9 − 1 0 − 11 M ) domain for heavy metals ( P b 2 + , C d 2 + , C u 2 + , Z n 2 + , A s 3 + Pb^{2+}, Cd^{2+}, Cu^{2+}, Zn^{2+}, As^{3+} P b 2 + , C d 2 + , C u 2 + , Z n 2 + , A s 3 + ).
Mechanism of Anodic Stripping Voltammetry (ASV)
ASV is a two-step hyphenated electrochemical process:
Preconcentration / Deposition Step (Cathodic Reduction):
The working electrode (typically a Hanging Mercury Drop Electrode HMDE or Thin Mercury Film Electrode TMFE on glassy carbon) is held at a constant cathodic deposition potential ( E dep E_{\text{dep}} E dep ) that is 200 − 400 mV 200-400\text{ mV} 200 − 400 mV more negative than the standard reduction potential of the analyte metal ions.
The solution is vigorously stirred (hydrodynamic transport) for a fixed period ( t dep = 1 − 10 minutes t_{\text{dep}} = 1-10\text{ minutes} t dep = 1 − 10 minutes ): M n + ( a q ) + n e − + H g ( l ) → electrochemical reduction M ( H g ) (amalgam) M^{n+}(aq) + ne^- + Hg(l) \xrightarrow{\text{electrochemical reduction}} M(Hg)\text{ (amalgam)} M n + ( a q ) + n e − + H g ( l ) electrochemical reduction M ( H g ) (amalgam)
Because the volume of the mercury drop or film is orders of magnitude smaller than the sample solution ( V Hg ≪ V soln V_{\text{Hg}} \ll V_{\text{soln}} V Hg ≪ V soln ), the metal analyte is concentrated into the mercury by a factor of 100 100 100 to 10 , 000 10,000 10 , 000 times its initial bulk solution concentration.
Quiet / Rest Period:
Stirring is stopped for 15 − 30 seconds 15-30\text{ seconds} 15 − 30 seconds to allow the solution to become quiescent and the concentration gradient in the mercury drop to homogenize.
Stripping Step (Anodic Sweep):
The working electrode potential is scanned anodically (positive direction) toward zero. As the potential reaches the formal oxidation potential of each amalgamated metal, the concentrated metal atoms are reoxidized and "stripped" back into solution: M ( H g ) → anodic oxidation M n + ( a q ) + n e − + H g ( l ) M(Hg) \xrightarrow{\text{anodic oxidation}} M^{n+}(aq) + ne^- + Hg(l) M ( H g ) anodic oxidation M n + ( a q ) + n e − + H g ( l )
Each metal generates a sharp current peak at its characteristic oxidation potential ( E p E_p E p ). The peak area (or peak height) is directly proportional to the original concentration of the metal in the sample. Cathodic Preconcentration (Stirred) --> Quiescent Rest --> Anodic Stripping Sweep
- Apply E_dep (-1.2 V vs. SCE) Hold E_dep Ramp Potential from -1.2 V to +0.2 V
- M^(n+) + ne- + Hg --> M(Hg) amalgam Stirring OFF M(Hg) --> M^(n+) + ne- (Sharp Peaks!)
- Coulometric Methods: Controlled-Potential vs. Coulometric Titrations
Coulometry measures the total quantity of electricity ( Q Q Q , coulombs) required to convert an analyte completely into a different oxidation state. Governed by Faraday's First and Second Laws of Electrolysis , coulometric analysis requires no calibration curves, chemical standards, or indicator titrations:
Q = ∫ 0 t i ( t ) d t = n F N = n F m M Q = \int_0^t i(t) \, dt = n \, F \, N = n \, F \, \frac{m}{M} Q = ∫ 0 t i ( t ) d t = n F N = n F M m
where F = 96485.3 C/mol e − F = 96485.3\text{ C/mol } e^- F = 96485.3 C/mol e − , n n n is stoichiometric electron transfer, m m m is mass of analyte (grams), and M M M is molar mass ( g/mol \text{g/mol} g/mol ).
Comparison of Coulometric Methodologies
Parameter Controlled-Potential Coulometry (Potentiostatic) Controlled-Current Coulometry (Coulometric Titration)
Electrical Control Working electrode potential held constant Current ( I I I ) held strictly constant
Current Profile Decays exponentially: i ( t ) = i 0 10 − k t i(t) = i_0 10^{-kt} i ( t ) = i 0 1 0 − k t Constant: i ( t ) = I i(t) = I i ( t ) = I
Charge Calculation Q = ∫ 0 ∞ i ( t ) d t Q = \int_0^\infty i(t) dt Q = ∫ 0 ∞ i ( t ) d t (electronic integrator) Q = I × t Q = I \times t Q = I × t (measured with precision electronic timer)
Selectivity Exceptional (only species active at E applied E_{\text{applied}} E applied react) Requires an auxiliary reagent to act as an intermediate titrant
Speed of Analysis Moderate to slow ( 15 − 60 minutes 15-60\text{ minutes} 15 − 60 minutes for complete electrolysis) Fast ( 1 − 5 minutes 1-5\text{ minutes} 1 − 5 minutes )
Standard Application Quantitation of transuranic actinides ( U , P u U, Pu U , P u ), separation of metals Karl Fischer moisture analysis; generation of halogens ( B r 2 , I 2 , C l 2 Br_2, I_2, Cl_2 B r 2 , I 2 , C l 2 )
The Coulometric Karl Fischer Titration for Trace Moisture
The coulometric Karl Fischer titration is the universal gold-standard method for determining trace moisture ( 1 ppm 1\text{ ppm} 1 ppm to 1 % 1\% 1% ) in pharmaceutical ingredients, organic solvents, and petrochemical fuels.
Reaction Chemistry: Water reacts quantitatively with iodine, sulfur dioxide, and a base (imidazole or pyridine, denoted B B B ) in methanol: H 2 O + I 2 + S O 2 + 3 B + C H 3 O H ⟶ 2 B H + I − + B S O 4 C H 3 − H_2O + I_2 + SO_2 + 3B + CH_3OH \longrightarrow 2BH^+I^- + BSO_4CH_3^- H 2 O + I 2 + S O 2 + 3 B + C H 3 O H ⟶ 2 B H + I − + BS O 4 C H 3 − Stoichiometry: Exactly 1 mole of I 2 1\text{ mole of } I_2 1 mole of I 2 consumes 1 mole of H 2 O 1\text{ mole of } H_2O 1 mole of H 2 O .
In-situ Coulometric Generation: Rather than adding liquid iodine titrant via burette, iodide ( I − I^- I − ) present in the electrolytic reagent is oxidized to iodine ( I 2 I_2 I 2 ) at a platinum generator anode at a constant current I I I : 2 I − → anode I 2 + 2 e − 2I^- \xrightarrow{\text{anode}} I_2 + 2e^- 2 I − anode I 2 + 2 e −
Because n = 2 n = 2 n = 2 electrons per molecule of water ( H 2 O ≡ I 2 ≡ 2 e − H_2O \equiv I_2 \equiv 2e^- H 2 O ≡ I 2 ≡ 2 e − ): m H 2 O = Q × M H 2 O n F = ( I × t ) × 18.015 g/mol 2 × 96485 C/mol m_{H_2O} = \frac{Q \times M_{H_2O}}{n F} = \frac{(I \times t) \times 18.015\text{ g/mol}}{2 \times 96485\text{ C/mol}} m H 2 O = n F Q × M H 2 O = 2 × 96485 C/mol ( I × t ) × 18.015 g/mol
Worked Example: A 2.500 mL 2.500\text{ mL} 2.500 mL aliquot of anhydrous methanol is analyzed for trace water contamination by coulometric Karl Fischer titration. A constant generator current of 64.32 mA 64.32\text{ mA} 64.32 mA ( 0.06432 A 0.06432\text{ A} 0.06432 A ) operates for 180.0 seconds 180.0\text{ seconds} 180.0 seconds to reach the biamperometric endpoint. Calculate the water concentration in the methanol sample in milligrams per liter ( mg/L \text{mg/L} mg/L ).
Step 1: Compute total electrical charge ( Q Q Q ): Q = I × t = 0.06432 A × 180.0 s = 11.5776 C Q = I \times t = 0.06432\text{ A} \times 180.0\text{ s} = 11.5776\text{ C} Q = I × t = 0.06432 A × 180.0 s = 11.5776 C
Step 2: Calculate mass of water consumed: m H 2 O = 11.5776 C × 18.015 g/mol 2 × 96485 C/mol = 208.5705 192970 g = 1.0808 × 10 − 3 g = 1.0808 mg m_{H_2O} = \frac{11.5776\text{ C} \times 18.015\text{ g/mol}}{2 \times 96485\text{ C/mol}} = \frac{208.5705}{192970}\text{ g} = 1.0808 \times 10^{-3}\text{ g} = 1.0808\text{ mg} m H 2 O = 2 × 96485 C/mol 11.5776 C × 18.015 g/mol = 192970 208.5705 g = 1.0808 × 1 0 − 3 g = 1.0808 mg
Step 3: Calculate concentration in mg/L \text{mg/L} mg/L : Concentration = 1.0808 mg 2.500 × 10 − 3 L = 432.3 mg/L (or ppm) \text{Concentration} = \frac{1.0808\text{ mg}}{2.500 \times 10^{-3}\text{ L}} = 432.3\text{ mg/L (or ppm)} Concentration = 2.500 × 1 0 − 3 L 1.0808 mg = 432.3 mg/L (or ppm)